David Harel. First-Order Dynamic Logic. LNCS 68. Springer-Verlag, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....correctness we (roughly) have to show that the procedures terminate and behave like the functions speci ed in SET. Correct behaviour can be characterized by a set of proof obligations (for details see again [Rei92a] These conditions are expressed in a sequent calculus for Dynamic Logic (DL, Har79] an extension of rst order logic by formulas h i ( diamond ) where is a program, and is again a DL formula. The intuitive meaning of h i is: terminates, and holds afterwards . This rough understanding of DL is sucient for the purpose of this paper. Sequents are denoted , ....

D. Harel. First Order Dynamic Logic. Springer LNCS, 1979.

....and rectified, leading to a better understanding of the dynamic domain and a better formalization of the problem. Several formalisms exist for reasoning about actions such as the situation calculus [23] action languages [6] the event calculus [13] the fluent calculus [26] and dynamic logic [10]. Since consistency is generally defined in terms of the associated deductive system and its properties generally require semantical consideration, a logic of action possessing a sound and complete deductive system would be most helpful in consistency analysis. Seen in this light, dynamic logic ....

D. Harel, First-order dynamic logic, LNCS 68, Springer-Verlag, 1979.

....in a Rationally Based Speech Act Theory Philip R. Cohen Artificial Intelligence Center Center for the Study of Language and Information SRI International 333 Ravenswood Ave. Menlo Park, CA 94025 and Hector J. Levesque t Department of Computer Science University of Toronto Abstract introduction A crucially important adequacy test of any theory of speech acts is its ability to handle performatives. This paper provides a theory of perfor matives as a test case for our rationally ....

....words [10] how do performatives work7 Any theory of illocutionary acts needs to provide a solution to questions such as these. But, such questions are not merely of theoretical interest. Natural language database questionanswering systems have been known to receive performative utterances [14] dialogue systems that recognize illocutionary acts (e.g. 6] will need to infer the correct illocutionary force to function properly, dialogue translation systems [5] will have to cope with markers of illocutionary 79 force that function performatlvely (e.g. sentence final particles in ....

[Article contains additional citation context not shown here]

D. Harel. First-Order Dynamic Logic. Springer-Verlag, New York City, New York, 1979.

....theorem of the logic is given. Properties of causal reasoning with the logic are discussed. i INTRODUCTION 2 1 Introduction Dynamic logic is one of the formalisms for specifying and reasoning about action and change that has been proposed explicitly or implicitly by several authors, such as [Harel 1979] [Rosenschein 1981] Kautz 1982] Giacomo and Lenzerini 1995] Prendinger and Schurz 1996] Castilho et al. 1999] in the last twenty years. There are some features of dynamic logic which distinguish it from the other formalisms of action. First, dynamic logic was originally developed for ....

....For instance, if a turkey is shot down, its death will cause the turkey to be unable to walk: alive causes walking. However, this can not be formally expressed in traditional dynamic logic. Obviously it can not simply wrotten as either alive walking or [alive]walking. The 1 See the preface of [Harel 1979]. 2Compound actions are actions generated fi om primitive actions by the program con nectives; J, first expression is unsuitable because it is equivalent to walking alive but alive causes walking does not mean walking causes alive . The second one is wrong because it is not allowed ....

D. Harel, First-order dynamic logic, LNCS 68, Springer-Verlag, 1979.

.... know what thime it is , we immediately obtain from the semantics the validity of formulas like 2: 30PM 3 6 85 De[ i 2: 30PM 3 6 85. The two basic temporal operators, Happens and Done, are augmented by some operators for describing the structure of event sequences, in the style of dynamic logic [28]. The two most important of these constructors are ; and a; a denotes a followed by a denotes a test action Here, the test must be interpreted as a test by the system; it is not a so called knowledge producing action that can be used by the agent to acquire knowledge. The ....

D. Harel. First-Order Dynamic Logic (LNCS Volume 68). Springer-Verlag: Berlin, Germany, 1979.

....using the existing action specifications but were unable to come up with a satisfactory result forcing the additional complexity. The policy language includes four action operators that allow various kinds of complex actions to be specified; sequence, non deterministic, once, and repetition [7]. Sequence : If A and B are actions, seq(A,B) denotes that action B must only be performed after action A or that action A and B must be performed in sequence. Non deterministic : If A and B are actions, nond(A,B) denotes a choice between A and B implying either A or B can be performed, but ....

D. Harel. First-Order Dynamic Logic. New York: SpringerVerlag, 1979.

....#, # : P rog(#, #, #, #) L(#, #, #, #) # (ModelW )L(#, W ) P rog(#, #, W ) # the language of the simple type theory, and D # is the solution of D = D D) i.e. the Scott domain. For the detail of languages, we will see later. For Dynamic Logics, see [16, 17, 12, 29, 18]. The point of theories of Dynamic Semantics is that they interpret expressions as state transitions. The most basic and logically refined framework of Dynamic Semantics is Groenendijk and Stokho# [14] s Dynamic Predicate Logic (DPL) To compare DPL with the Tarskian static semantics, firstly I ....

David Harel. First-Order Dynamic Logic. Springer-Verlag, Berlin, 1979.

....between motions and PVMs, which is a formalization of the invariance of the truth of a motion independent of viewpoints, called the viewfinder invariance . In section 6, I will explain empthay as a viewfinder resetting actions. II. First Order Concurrent Dynamic Logic (CDL) Dynamic Logics [7], 8] 9] 10] 11] are modal logics of which modal operators express programs or actions. CDL is a dynamic logic, defined as follows [9] Definition 1: Let L = Rel Fun Con V ar be an alphabet made up of disjoint sets of relation symbols (R Rel) function symbols (f Fun) individual ....

David Harel, First-Order Dynamic Logic, Springer-Verlag, Berlin, 1979.

....PDLcF, namely PDLL. In this fragment we restrict the admissible set of programs to include only a fragment L of the linear context free programs. In this fragment, only productions of the form X aXb X a for nonterminals X and terminals (including ) a and b. In this choice we follow Harel [9], who uses exactly the same set of programs to describe the first order Dynamic Logic with respect to this set. The definition of the set II follows [9] closely. The reason behind this choice is that the theory would become too cumbersome and technical details would block the view on underlying ....

....fragment, only productions of the form X aXb X a for nonterminals X and terminals (including ) a and b. In this choice we follow Harel [9] who uses exactly the same set of programs to describe the first order Dynamic Logic with respect to this set. The definition of the set II follows [9] closely. The reason behind this choice is that the theory would become too cumbersome and technical details would block the view on underlying prindples. PDLL is formally defined as follows. Let o and lIo be sets of primitive predicates and programs, respectively. That is, o = po, IIo = ao, ....

[Article contains additional citation context not shown here]

Harel, D., First Order Dynamic Logic, LNCS 68, Springer-Verlag, Berlin etc., 1979.

....contain statements or instructions to express what has to be done. In other words programs express how certain actions involving (the hardware of) the computer should be performed. To reason about programs, special logics have been developed such as Hoare s logic and dynamic logic ( Hoa69] [Har79]) Also temporal logic has been employed for this purpose (see e.g. Kr087] MP92] In some way one might view temporal logic as a dynamic logic in which one abstracts away from the particular actions that take place, and only considers the flow of time while executing a program. On the other ....

D. Harel, First-Order Dynamic Logic, Springer-verlag, Berlin, 1979.

....more detailed modalities. It is taken into consideration that, when reasoning about processes, different relationships between actions and states have to be investigated: an action is performed and some property will hold, or if an action is performed, then some property will hold. Dynamic Logic [Har79] is also based on labeled Kripke structures, although it is quite different: Both its modalities query only the action carried out in the next step, corresponding to the focus of DL on program verification. A logic more similar to MCTL, ACTL, has been presented in [DV90] ACTL is a modal logic ....

....logic formulas. 3. 1 MCTL: Extension of CTL to Labeled Kripke Structures MCTL is an extension of first order CTL to labeled Kripke structures, integrating the language of action formulas as defined above into first order CTL: The modal operators are labeled in the style of Dynamic Logic [Har79], HennessyMilner Logic HML [HM85] or ACTL [DV90] with action formulas querying the respective transitions. An examination of ACTL, which uses the same modalities as CTL, shows that its (labeled) nexttime operator, X, is not its own dual, as it is in CTL: ffi CTLF ) ffi CTL ( F ) but ....

D. Harel. First-Order Dynamic Logic, volume 68 of LNCS. Springer, 1979.

....contain statements or instructions to express what has to be done. In other words programs express how certain actions involving (the hardware of) the computer should be performed. To reason about programs, special logics have been developed such as Hoare s logic and dynamic logic ( Hoa69] [Har79]) Also temporal logic has been employed for this purpose (see e.g. Kr687] IMP92] In some way one might view temporal logic as a dynamic logic in which one abstracts away from the particular actions that take place, and only considers the flow of time while executing a program. On the other ....

....PDeL, introduced in [Mey88] is a version of dynamic logic especially tuned to use as oughtto do style deontic logic. It is based on the idea of Anderson s reduction of ought to be style deontic logic to alethic modal logic, but instead it reduces ought to do deontic logic to dynamic logic ([Har79]) The basic idea is very simple: some action is forbidden if doing the action leads to a state of violation. In a formula: F def [t]V, where the dynamic logic formula [oqtp denotes that execution performance of the action leads (necessarily) to a state (or states) where tp holds, and V is a ....

D. Harel, First-Order Dynamic Logic, Springer-verlag, Berlin, 1979.

....consisting of a particular agent s execution of an action. We let (i) indicate that agent i performs the action . We can reason about the results of actions on both a private level and a global level. The global level reasoning is the standard one using dynamic logic as described by Harel in [11]. We use [ i) to indicate that if agent i performs the action indicated by the result will be . i.e. no matter what happens, if agent i performs the system will change to a state where holds. Note that this is a very strong statement No unforeseen action can disturb the execution of ....

D. Harel. First Order Dynamic Logic. LNCS 68 Springer, 1979.

....conversions) we use arbitrary large integers for Java integers. The reason is that JavaCard does not support integers, so that integer over ows cannot occur. Of course, it is simple to add bounded integers to out speci cation, if it is useful. 9 3.1. 2 Dynamic Logic We use a dynamic logic (DL, Har79] for the veri cation of JavaCard programs. DL extends rst order logic with two modal operators, a box [ and a diamond h:i : The box (diamond) contains a program, afterwards follows again a DL formula. In our case, the box (diamond) contains a pair of a variable for the store and a Java ....

D. Harel. First Order Dynamic Logic. LNCS 68. Springer, Berlin, 1979.

....a formalism for representing and specifying both the direct and indirect effects of actions in a unified logical structure. Our framework is based on dynamic logic. We do so not only because the dynamic logic is one of the typical formalisms for reasoning about action (c.f. the preface of [Harel 1979]) but also because the modal expression of causal relation is one of the main approaches to causation in philosophy ( Brand 1976] and in AI ( McCain and Turner 1995;Giordano et al. 2000] In dynamic logic, causation between an action and its effects is expressed by the modal formula [ A, where ....

D. Harel, First-order dynamic logic, LNCS 68, Springer-Verlag, 1979.

.... [23] There are two key issues at stake in any formalism for temporal projection: the choice of representation of temporal objects and the underlying logical language (the two are obviously interrelated) Dynamic logic as a formalism for reasoning about action was proposed twenty years ago [8, 21, 10]. However, classical dynamic logic as originally proposed [18] can only reason forwards in time. For instance, A means A is true after performing action . If we view [ as a temporal modality, some properties of [ are identical to those of the future modality [F ] More precisely, acts ....

....can be generated from atomic programs. If , are programs, means execute followed by , means execute either or nondeterministically , means repeat nite times nondeterministically . A is a special program, meaning test A proceed if A is true, else fail [8] [6] The alphabet of the language L TPDL consists of countable sets Flu; ActP of uent and primitive action symbols respectively. Formulas (A 2 Fma) and actions ( 2 Act) are de ned by the following BNF rules: A : f j :A j A 1 A 2 j [ A j [ 1 A : a j 1 ; 2 j 1 [ 2 j ....

D. Harel. First-order dynamic logic,, Springer-Verlag, 1979.

....the logical system itself and the action description of the dynamic system under consideration needs to be evaluated. Several formalisms exist for reasoning about actions such as the situation calculus [19] action languages [7] the event calculus [13] the uent calculus [21] and dynamic logic [12]. Since consistency is generally de ned in terms of the associated deductive system and its properties generally require semantical consideration, a logic of action possessing a sound and complete deductive system would be most helpful in consistency analysis. Seen in this light, dynamic logic ....

D. Harel. First-order dynamic logic,, Springer-Verlag, 1979.

....i A E i B (The (T) schema captures the intuition that if agent i brings it about that A, then A is indeed the case; that is, E i is a success operator. This approach to the logic of action offers an expressive power rather different from that of action logics based on dynamic logic (see e.g. [16] [17] for instance, it facilitates the expression of the different atomic positions an agent might be in with respect to a particular state of affairs A: E i A, E i A and E i A E i A ( i remains passive with respect to A ) and it readily affords a means of characterising cases of interpersonal ....

D. Harel, First-Order Dynamic Logic, LNCS 68, Springer, 1979.

....we use arbitrary large integers for Java integers. The reason is that JavaCard does not support integers, so that integer overflows cannot occur. Of course, it is simple to add bounded integers to out specification, if it is useful. 9 3.1. 2 Dynamic Logic We use a dynamic logic (DL, Har79] for the verification of JavaCard programs. DL extends first order logic with two modal operators, a box [ and a diamond #.# . The box (diamond) contains a program, afterwards follows again a DL formula. In our case, the box (diamond) contains a pair of a variable for the store and a Java ....

D. Harel. First Order Dynamic Logic. LNCS 68. Springer, Berlin, 1979.

....complications, depending on the use to which the taxonomy is put. For logical theories, one important question is whether the logic can accommodate simultaneous action or level generation (Goldman, 1970) Simple versions of, e.g. the situation calculus (McCarthy and Hayes, 1969) or dynamic logic (Harel, 1979) do not, which makes it difficult to formalize this kind of phenomenon. Likewise, within dialogue systems, reasoning about act occurrence is often made not on the basis of necessary and sufficient conditions, but on closeness of fit, using abductive or statistical methods. Such methods generally ....

Harel, D. (1979). First Order Dynamic Logic. Springer-Verlag.

....logic we are interested in is an extension of the standard multimodal logic. In the standard multi modal logic one has just nitely many pairs of necessity and possibly operators. In our version we allow relational terms as parameters of the modal operators, almost like in dynamic logic [5], but without the operator and the test operator. 5 De nition 3.1 (Syntax of Multi Modal Logic LMM ) LMM formulae are like modal logic formulae, but the modal operators are parameterized with LRA terms. LMM = P j LMM LMM j LMM LMM j :LMM j [LRA ]LMM j hLRAiLMM where P is a nite ....

D. Harel. First-Order Dynamic Logic. Lec. Notes in Comp. Sci. 68, Springer-Verlag, 1979.

....point of view. Not as much attention, however, has been payed to its proof theory or to the possibility of representing consequence relations di#erent from that of validity. The relevant concept being that of theoremhood, the proof systems considered have been mainly Hilbert style systems [7, 8, 15, 26]. There is only one remarkable exception, albeit unpublished, of ND style System for Deterministic DL due to C. Stirling [25] see Sect.5) Besides absolute validity and absolute truth, various CR s can be introduced according to the class of models that one focuses on. Since in this paper we ....

....an environment for the development of verified software. In the tradition of the Edinburgh LCF, KIV provides a metalanguage which can be used for representing both the logic as well as the tactics and strategies for proof search and proof management. KIV is an Hilbert style proof system: as in [7, 15], Dynamic Logic is axiomatised by means of several axioms and few rules. User defined strategies and tactics make this unnatural calculus more user friendly. The intended consequence relation of KIV is that of validity, not that of truth. As a consequence of this, KIV does not enjoy the Deduction ....

D. Harel. First-Order Dynamic Logic. No.68 in LNCS. Springer-Verlag, 1979.

....in all nal states of , and h i expresses that holds in some nal state of . In versions of DL with a non deterministic programming language there can be several such nal states (worlds) Here we consider a Deterministic Dynamic Logic (DDL) with a deterministic while programming language [4, 6]. For deterministic programs there is exactly one nal world (if terminates) or there is no nal world (if does not terminate) The formula h i is valid if, for every state s satisfying pre condition , a run of the program starting in s terminates, and in the terminating state the ....

....states. In Temporal Logics, however, the program is xed and considered to be part of the structure over which the formulas are interpreted. Temporal Logics, therefore, do not have the compositionality of Dynamics Logics. The calculus for DDL described in [6] which is based on the one given in [4]) has been implemented in the software veri cation systems KIV [11] and VSE [7] It has successfully been used in practice to verify software systems of considerable size. The work reported here has been carried out as part of the KeY Projekt [1] 1 The goal of KeY is to enhance a commercial ....

[Article contains additional citation context not shown here]

D. Harel. First-order Dynamic Logic. LNCS 68. Springer, 1979.

....of a set F lu of uent symbols (propositional variables) and a set Act P of primitive action symbols. We will use f , with possible subscripts, to denote uents, and use a, with possible subscripts, for primitive actions. The formulas (A 2 Fma) and actions ( 2 Act) can be de ned as usual (see [15, 21, 13]) A formula which does not include modal operators is referred to as a propositional formula ( 2 Fma P ) The semantics and deductive system of PDL can be found in any standard introductory text e.g [13] 2.1 Action description Classical PDL is not adequate for reasoning about action or more ....

D. Harel, First-order dynamic logic, LNCS 68, Springer-Verlag, 1979.

.... property of normal modal logics has been intensively investigated in recent years with positive results( Maksimova 1991;Madarasz 1995;Marx 1999] 2 Reasoning with action description in PDL Reasoning about action is one of the motivations the dynamic logic was proposed (see the preface of [Harel 1979]) In dynamic logic, effects of actions are expressed by modal formulas. A represents always causes A , where is 1 Some action logics are first order or have some fragment which is first order. This does not mean that such a logic has the interpolation property. 2 We are told that it ....

....h i represents is executable. In this paper, we will only use the propositional dynamic logic (PDL) A language of PDL consists of a set Flu of fluent symbols(propositional variables) and a set ActP of primitive action symbols. The formulas (Fma) and actions (Act) can be defined as usual (c. f. [Harel 1979;Kozen and Tiuryn 1990] Particularly, a formula which does not include modal operators is referred to as propositional formula ( 2 FmaP ) The semantics and deductive system of PDL can be found in any dynamic logic book. Note that the classical dynamic logic is not adequate for reasoning about ....

D. Harel, First-order dynamic logic, LNCS 68, Springer-Verlag, 1979.

....a formalism for representing and specifying both the direct and indirect effects of actions in a unified logical structure. Our framework is based on the dynamic logic. We do so not only because the dynamic logic is one of the typical formalism for reasoning about action (c.f. the preface of [Harel 1979]) but also because the modal expression of causal relations is one of the main approaches to causation in philosophy ( Brand 1976] and in AI ( McCain and Turner 1995;Giordano et al. 2000] In dynamic logic, the causal relation between an action and its effects is expressed by the modal formaula ....

D. Harel, First-order dynamic logic, LNCS 68, Springer-Verlag, 1979.

....node d is not allocated in the second interpreter. 3 Dynamic Logic and Algebraic Speci cations The KIV system uses another formalism to describe pseudocode over abstract data : Imperative Programs over Algebraic Speci cations. To prove properties over these programs, we use Dynamic Logic (DL,[Har79], Gol82] DL is an extension of (in our case many sorted) rst order logic by formulas h i (read diamond ) and [ box ) where is an imperative program, and is again a DL formula. The intuitive meaning of the rst formula is terminates and afterwards holds , the second ....

D. Harel. First Order Dynamic Logic. Springer LNCS, 1979.

....theorem of the logic is given. Properties of causal reasoning with the logic are discussed. 1 INTRODUCTION 2 1 Introduction Dynamic logic is one of the formalisms for specifying and reasoning about action and change that has been proposed explicitly or implicitly by several authors, such as [Harel 1979] [Rosenschein 1981] Kautz 1982] Giacomo and Lenzerini 1995] Prendinger and Schurz 1996] Castilho et al. 1999] in the last twenty years. There are some features of dynamic logic which distinguish it from the other formalisms of action. First, dynamic logic was originally developed for ....

....instance, if a turkey is shot down, its death will cause the turkey to be unable to walk: alive causes :walking. However, this can not be formally expressed in traditional dynamic logic. Obviously it can not simply wrotten as either :alive :walking or [ alive] walking. The 1 See the preface of [Harel 1979]. 2 Compound actions are actions generated from primitive actions by the program connectives ; 2 EXTENDED PROPOSITIONAL DYNAMIC LOGIC 3 rst expression is unsuitable because it is equivalent to walking alive but :alive causes :walking does not mean walking causes alive . The ....

D. Harel, First-order dynamic logic, LNCS 68, Springer-Verlag, 1979.

....how the above examples can be modelled in our logic. Section 5 is used to draw some conclusions. 2 A logic of actions and norms We now proceed with the definition of a set of formulas with which we can describe the behaviour of (interpreted) actions. This language is a variant of dynamic logic ([5]) and was first used for this purpose in [6] In the present paper we add a few new formulas to this language. They are the ones defined in points (5) and (6) below. The formulas defined in (5) all involve some type of temporal operations on actions. The formulas defined in (6) define the ....

D. Harel. First Order Dynamic Logic. LNCS 68 Springer, 1979.

....of events describable by an action expression a will happen next or has just happened, respectively. Versions of HAPPENS and DONE specifying the agent (x) are also defined. An action expression here is built from variables ranging over sequences of events using the constructs of dynamic logic [4]: a;b is action composition; ajb is nondeterministic choice; ajjb is concurrent occurrence of a and b; p is a test action; and finally, a is repetition. The usual programming constructs such as IF THEN actions and WHILE loops, can easily be formed from these. Because test actions occur ....

D. Harel. First-Order Dynamic Logic. Springer-Verlag, New York City, New York, 1979.

....in Logics of Programs Andrzej Szalas Institute of Informatics University of Warsaw PKiN VIIIp. 00 901 Warsaw, Poland Abstract We introduce and discuss a notion of strictly arithmetical completeness related to relative completeness of Cook [4] and arithmetical completeness of Harel [5]. We present a powerful technique of obtaining strictly arithmetical axiomatizations of logics of programs. Given a model theoretic semantics of a logic, and a set of formulae de ning (in a meta language) its non classical connectives we automatically derive strictly arithmetically complete and ....

....proof systems that enable formal reasoning about program properties. First order logics of programs that are intended to express at least the most basic properties of programs as e.g. halting property, cannot be characterized completely (in classical sense) by nitistic proof systems (cf. e.g. [1,3,5,13,15]) On the other hand, in order to stay within a nitary framework, This work was supported by grant RP.I.09 of Polish Ministry of National Education. 1 one can try to weaken classical notion of completeness. Various non classical notions of completeness were de ned and new completeness ....

[Article contains additional citation context not shown here]

Harel D.: First-Order Dynamic Logic, LNCS 68, Springer-Verlag 1978.

....modules, thus providing a faithful formalisation of the notion of object. The chosen logic satisfies these requirements, and follows previous work on action, deontic and temporal logics (eg, 15,17,18,20,33,34] Basically, a combination of modal (action) operators (as in dynamic logic [29]) and of deontic predicates of permission and obligation on actions is used to describe and prescribe behaviour as suggested in [34] and temporal operators are used to reason about the safety and liveness properties of the described objects following [15] It will not be possible to give a full ....

D. Harel, First-Order Dynamic Logic, LNCS 68, Springer-Verlag 1979

....j= 3.1 Some Validities In this section, we list a few validities. The rst validity in the lemma below expresses that tests are used to introspect the beliefs of the agent. The other two validities are the usual axioms for sequential composition and nondeterministic choice from dynamic logic [1]. The axiom for sequential composition expresses that if after executing 1 ; 2 necessarily holds, then necessarily after executing 1 we know that in case 2 is executed consecutively will hold, and vice versa. The axiom for nondeterminism states that only if after execution of both 1 ....

David Harel. First-order dynamic logic. LNCS 68. Berlin: Springer, 1979.

....order to obtain other values. See [43] for an interesting discussion on the differences between values and objects in Computing. The way the actions update the attributes is specified through axioms of the form ############################# The (modal) operators ######## are as in dynamic logic [34] (see also [39] for the use of these operators for database specification) except that they are applied herein to terms rather than formula [23] by ################# we denote the value that ######### takes after the denotation of ###### occurs. The intuition here is that terms (such as ....

D.Harel, First-Order Dynamic Logic, LNCS 68, Springer-Verlag 1979

...., namely PDLL . In this fragment we restrict the admissible set of programs to include only a fragment L of the linear context free programs. In this fragment, only productions of the form X aXb X a for nonterminals X and terminals (including ffl) a and b. In this choice we follow Harel [9], who uses exactly the same set of programs to describe the first order Dynamic Logic with respect to this set. The definition of the set Pi follows [9] closely. The reason behind this choice is that the theory would become too cumbersome and technical details would block the view on underlying ....

....fragment, only productions of the form X aXb X a for nonterminals X and terminals (including ffl) a and b. In this choice we follow Harel [9] who uses exactly the same set of programs to describe the first order Dynamic Logic with respect to this set. The definition of the set Pi follows [9] closely. The reason behind this choice is that the theory would become too cumbersome and technical details would block the view on underlying principles. 47 PDLL is formally defined as follows. Let Phi 0 and Pi 0 be sets of primitive predicates and programs, respectively. That is, Phi 0 = ....

[Article contains additional citation context not shown here]

Harel, D., First Order Dynamic Logic, LNCS 68, Springer-Verlag, Berlin etc., 1979.

.... also be observed when defining the nesting of sets [BNST, ShNa] Updates were defined so as to allow the full use of these constructs in rules and to support the notion of database transactions [NaKr] The di#cult problem of formalizing their semantics was solved through the use of dynamic logic [Har]. The semantics so defined reduces to first order logic in the absence of updates. Finally, the notion of functional dependencies was used to support nondeterminism through a construct called choice [KrN1] 2.2 The Compilation Problem The LDL compiler performs several functions, beginning ....

Harel, D., "First-Order Dynamic Logic," Lecture Notes in Computer Science, (G. Goos and J. Hartmanis, eds.), Springer Verlag, 1979.

....for a high level nondeterministic program. This is the core idea of the research carried on by Levesque et. al [9] 3 [1] presents a survey on the deductive planning field. which uses situation calculus [11, 8] as the basis of a programming language for steering robots. Based on dynamic logic [7], Stephan Biundo [14] use a similar approach, although they are more concerned with the data structures inherent to world situations. As far as the modeling of changes in the world is concerned, the majority of works based on deductive planning address this issue via the axiomatization of action ....

D. Harel. First Order Dynamic Logic. Springer LNCS 68, 1979.

....modal logic as de ned in [9, 10] the most primitive actions, called private actions, are represented by propositions. In the logic no explicit and distinct representation for actions is present nor are there any modalities for actions incorporated into the logic as in, for example, dynamic logic ([2]) In [5] in particular this feature is criticised. The speci c axioms of the logic which are proposed in [9] turn out to have the highly counter intuitive consequence that if an agent cannot do something, then it believes that it can do it. To secure consistency within the logic, as a ....

David Harel. First-order dynamic logic. LNCS 68. Berlin: Springer, 1979.

....(1982) outlines such a model in detail and discusses its application to AI reasoning problems. Another common temporal representation, variants of which are found in philosophy, linguistics (e.g. tense logic, Prior (1967) and theoretical computer science (e.g. dynamic logic, Pratt, 1978, Harel, 1979), involve modal tense operators. Rather than having explicit time in the logic, modal operators such a PAST are introduced. Thus the formula PAST(Green(Frog1) means that FROG1 was green sometime in the past. A similar operator can be defined for Future, and in models that use discrete time, an ....

Harel, D. (1979) First-Order Dynamic Logic, Springer-Verlag, NY.

.... and complexity) Much of this introductory material as it pertains to DL can be found in the authors text [Harel et al. 2000] There are by now a number of books and survey papers treating logics of programs, program verification, and Dynamic Logic [Apt and Olderog, 1991; Backhouse, 1986; Harel, 1979; Harel, 1984; Parikh, 1981; Goldblatt, 1982; Goldblatt, 1987; Knijnenburg, 1988; Cousot, 1990; Emerson, 1990; Kozen and Tiuryn, 1990] In particular, much of this chapter is an abbreviated summary of material from the authors text [Harel et al. 2000] to which we refer the reader for a more ....

....forms of the consequence problem, studied in [Parikh, 1981] First order DL was defined in [Harel et al. 1977] where it was also first named Dynamic Logic. That paper was carried out as a direct continuation of the original work of [Pratt, 1976] Many variants of DL were defined in [Harel, 1979] . In particular, DL(bstk) is very close to the context free Dynamic Logic investigated there. Uninterpreted reasoning in the form of program schematology has been a common activity ever since the work of [Ianov, 1960] It was given considerable impetus by the work of [Luckham et al. 1970] and ....

[Article contains additional citation context not shown here]

D. Harel. First-Order Dynamic Logic, volume 68 of Lect. Notes in Comput. Sci. Springer-Verlag, 1979.

No context found.

David Harel. First-Order Dynamic Logic. LNCS 68. Springer-Verlag, 1979.

No context found.

Harel, D., 1979. First Order Dynamic Logic, Berlin: Springer-Verlag.

No context found.

D. Harel. First-Order Dynamic Logic (LNCS Volume 68). Springer-Verlag: Berlin, Germany, 1979.

No context found.

Harel, D., First-Order Dynamic Logic, LNCS, 68, Springer-Verlag, 1979.

No context found.

D. Harel. First-order Dynamic Logic. Springer-Verlag, LNCS 68, 1979.

No context found.

D. Harel. First Order Dynamic Logic. Springer, 1979.

No context found.

D. Harel. First Order Dynamic Logic. LNCS 68 Springer-Verlag, Heidelberg, 1979.

No context found.

D. Harel, First-Order Dynamic Logic, Springer-verlag, Berlin, 1979.

No context found.

Harel, D. (1979). First-order Dynamic Logic. LNCS 68. Springer.

No context found.

Harel, D., First Order Dynamic Logic, LNCS 68, Springer-Verlag, Berlin etc., 1979.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC